1. Field of the Invention
The invention relates to a method and a system for generating a one-dimensional spline waveform, the one-dimensional spline waveform being a function of a position on a screen of a display device in one direction, the method comprising the steps of: generating, from a position information indicating the position on the screen, a position address, the position address indicating a number of a section and a relative position indicating a position within the section for virtually partitioning the screen in sections in the one direction; calculating, in each section, from the relative position and a set of sub-function coefficients, a sub-function being a polynomial for obtaining the one-dimensional spline waveform being a chain of consecutive sub-functions in corresponding consecutive section; and converting, in each section, predetermined values into the sub-function coefficients.
The invention also relates to a method for generating a two-dimensional spline waveform, the two-dimensional spline waveform being dependent on a position in a first and a second direction on a screen of a display device, the display device being scanned in a raster of lines, the first and the second direction being substantially perpendicular.
Such a waveform may be used for correcting deflection errors of a display tube, such as convergence errors or east-west distortions. Such a waveform may also be used as a dynamic focusing waveform, or as a waveform influencing the brightness of a displayed picture to compensate for brightness non-uniformity on a display device.
2. Description of the Related Art
It is known that a quadratic spline waveform, which extends along the whole width or hight of a picture tube screen, and which is a function of a position address, can be generated as a chain of sections of second order sub-functions of the position address. Input coefficients (the predetermined values) are stored in a memory and are referred to as stored values. If n stored values are available, n-2 second order sub-functions can be generated each in one of n-2 sections. The first second order sub-function is fully determined by 3 of the stored values, and a succeeding second order sub-function in a succeeding section is determined by only one stored value, as 2 conditions are already fixed by the demand that the resulting quadratic spline waveform must have a value, and a first derivative which are continuous in every point, so also at the boundary of the two consecutive sections. This follows from the definition of a p-th order spline function, viz. a function which is, and whose first thru (p-1)-th derivatives are continuous in every point. The quadratic spline waveform is generated as follows:
in a first section, a first parabola function is calculated at desired positions determined by the position address, and by using three of the stored values as parabola coefficients (f.sub.1 (x)=a0+a1.x+a2.x.sup.2). The stored values are adjustable to obtain a shape of the parabola sections fitting the needed correction on the picture tube screen, in every further section, a further parabola is calculated at wished positions determined by the position address using only one stored value not yet used, and by calculating the parabola coefficients out of that one stored value and the two equations determined by the fact that at the border of two succeeding sections, the value and the first derivative of the parabola functions in these sections have to be equal. Hence, two of the parabola coefficients of a succeeding section will depend on coefficients of preceding sections. The calculation of the parabola coefficients from the stored values becomes more and more complex every further section.
It is a disadvantage of the known way of generating a quadratic spline waveform that in each section, a different program of a computer or different hardware circuits are needed for converting the stored values into parabola coefficients. The most complex calculation in the last section determines the complexity of the program or the hardware circuits. Further, this complex calculation may need too much time to perform the calculations in real time without storing the sub-function coefficients or intermediate results. A further drawback is that the one extra coefficient used in every section determines the second derivative of the sub-function in this section. The generated quadratic spline waveform will deviate from an intended waveform if this coefficient has been determined slightly wrong. The deviation will influence the generated quadratic spline waveform in all further sections.